YouTipMd Math
### LaTeX Math Formulas Basics
In Markdown, math formulas are expressed using LaTeX syntax. LaTeX is a powerful typesetting system, especially suitable for documents containing complex math formulas.
#### Basic Syntax Structure
* **Commands**: Start with a backslash ``, such as `alpha`, `sum`
* **Parameters**: Enclosed in curly braces `{}`, such as `frac{a}{b}`
* **Subscript**: Use `_`, such as `x_1`
* **Superscript**: Use `^`, such as `x^2`
* **Grouping**: Use curly braces to combine multiple characters, such as `x_{i+1}`
#### Common LaTeX Commands
alpha, beta, gamma % Greek letters sum, prod, int % Summation, product, integral frac{numerator}{denominator} % Fraction sqrt{Expression} % Square root sqrt{Expression} % nth root
### Inline Formulas and Block Formulas
#### Inline Formulas
Inline formulas are enclosed with single dollar signs `$`, and the formula will be embedded in the text, such as: Variables in text $x = 5$ and function $f(x) = x^2 + 2x + 1$.
Variables in text $x = 5$ and function $f(x) = x^2 + 2x + 1$.
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#### Block Formulas
Block formulas are enclosed with double dollar signs `$$`, and the formula will be displayed as a separate centered line:
E = mc^2
int_{-infty}^{infty} e^{-x^2} dx = sqrt{pi}
$$E = mc^2$$ $$int_{-infty}^{infty} e^{-x^2} dx = sqrt{pi}$$
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#### Multi-line Formulas
Use the `align` environment to create multi-line aligned formulas:
begin{align}
f(x) &= ax^2 + bx + c
f'(x) &= 2ax + b
f''(x) &= 2a
end{align}
$$ begin{align} f(x) &= ax^2 + bx + c f'(x) &= 2ax + b f''(x) &= 2a end{align} $$
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## Common Math Symbols
### Basic Operation Symbols
* Addition, subtraction, multiplication, division: `+`, `-`, `times`, `div`
* Fractions: `frac{a}{b}` β $frac{a}{b}$
* Roots: `sqrt{x}`, `sqrt{x}` β $sqrt{x}$, $sqrt{x}$
* Exponents: `x^2`, `e^{ipi}` β $x^2$, $e^{ipi}$
### Comparison Symbols
* Equals: `=`, `neq`, `equiv` β $=$, $neq$, $equiv$
* Greater/Less: ``, `leq`, `geq` β $$, $leq$, $geq$
* Approximately: `approx`, `sim` β $approx$, $sim$
### Set Symbols
* Belongs to: `in`, `notin` β $in$, $notin$
* Contains: `subset`, `supset` β $subset$, $supset$
* Intersection/Union: `cap`, `cup` β $cap$, $cup$
* Empty set: `emptyset` β $emptyset$
### Greek Letters
Common Greek letters and their LaTeX representations:
| Lowercase | Uppercase | LaTeX | Lowercase | Uppercase | LaTeX |
| --- | --- | --- | --- | --- | --- |
| Ξ± | Ξ | `alpha` | Ξ½ | Ξ | `nu` |
| Ξ² | Ξ | `beta` | ΞΏ | Ξ | `o` |
| Ξ³ | Ξ | `gamma` | Ο | Ξ | `pi` |
| Ξ΄ | Ξ | `delta` | Ο | Ξ‘ | `rho` |
| Ξ΅ | Ξ | `epsilon` | Ο | Ξ£ | `sigma` |
| ΞΈ | Ξ | `theta` | Ο | Ξ€ | `tau` |
| Ξ» | Ξ | `lambda` | Ο | Ξ¦ | `phi` |
| ΞΌ | Ξ | `mu` | Ο | Ξ© | `omega` |
### Special Functions and Symbols
* Trigonometric functions: `sin`, `cos`, `tan`
* Logarithms: `log`, `ln`
* Limits: `lim_{x to 0}`
* Summation: `sum_{i=1}^{n}`
* Integration: `int_{a}^{b}`
* Infinity: `infty`
### Matrix Representation
Use the `matrix` environment:
begin{pmatrix}
a & b
c & d
end{pmatrix}
$$ begin{pmatrix} a & b c & d end{pmatrix} $$
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Matrices with different bracket types:
* `pmatrix`: parentheses $begin{pmatrix} a & b c & d end{pmatrix}$
* `bmatrix`: square brackets $begin{bmatrix} a & b c & d end{bmatrix}$
* `vmatrix`: determinant $begin{vmatrix} a & b c & d end{vmatrix}$